UNIVERSITY
OF WROC£AW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 23, Fasc. 2,
pages 251 - 272
 

DISTRIBUTIONS OF SUPREMA OF LÉVY PROCESSES VIA THE HEAVY TRAFFIC INVARIANCE PRINCIPLE

W. Szczotka
W. A. Woyczyński

Abstract: We study the relationship between the distribution of the supremum functional M = sup (X(t)- bt) X 0<t<o o for a process X with stationary, but not necessarily independent increments, and the limiting distribution of an appropriately normalized stationary waiting time for G/G/l queues in heavy traffic. As a by-product we obtain explicit expressions for the distribution of M X in several special cases of Lévy processes.

2000 AMS Mathematics Subject Classification: 60K25, 60G10, 60G18, 60E07.

Key words and phrases: Lévy process, supremum, heavy traffic, queueing systems.

Download:    Abstract    Full text   Abstract + References